Is it permissible to complete dental treatment and request an invoice with a deferred date for next year, or to defer payment and request the invoice at the time of payment, due to exceeding the maximum insurance limit for the current year?

If the insurance is a permissible Takaful (cooperative) insurance, then its terms must be adhered to, and it is not permissible to circumvent them. However, if it is commercial insurance, then it is not permissible to subscribe to it from the outset, and it is not permissible to benefit from it except to the extent of the premiums paid.